Orientation Estimation of Cryo-EM Images for Molecules with Arbitrary Symmetry by Semidefinite Programming

arXiv:2610.18691v1 Announce Type: new Abstract: This paper extends the non-unique games framework introduced in Bandeira et al. (2020) to address symmetric structures. Precisely, we consider the problem [ egin{aligned} nderset{g_1,ldots,g_nin G}{operatorname{min}},, frac{1}{|S|}sum_{i,j=1}^n sum_{sin S} f_{ij}(g_i s g_j^{-1}), end{aligned} ] where G is a compact group, Ssubset G is a finite subgroup of symmetry elements, and f_{ij}:Grightarrow R is a loss function. A notable example is common lines based orientation estimation of cryo-EM images for molecules with point group symmetry S, where G is the rotation group operatorname{SO}(3). With a semidefinite programming relaxation, we turn the problem into a convex program that is solved with the alternating direction method of multipliers. Unlike existing approaches which are tailored to specific symmetry groups, ours provides a unified computational framework for addressing all point group symmetries. We demonstrate the applicability of the proposed algorithm on the cryo-EM orientation estimation problem on both simulated and experimental datasets. In particular, our algorithm is effective in generating high-quality ab initio models from only a few class averages computed from experimental images.

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Source: arXiv cs.CV | 2026-10-14